The technological breakthroughs of the last few decades establish the conditions under which diverse items, resources, and operations are made increasingly fungible and combinable with one another. We link this wider ecology of recombination to the formation of what we call layered modular architectures whereby content, apps, software, and hardware can be brought to recombinant configurations that cross the boundaries of established products and industries and redefine the rigid divide between upstream design and downstream use. These developments, we suggest, qualify and expand the longstanding understanding of innovation as recombinant. We extend these ideas to include the examination of the critical importance that data have recently acquired. We consider the functions which digital data perform in a variety of contexts, including organizations, markets, societal sectors, and the training of AI systems. We contrast the analytic and narrative nature of innovation brought about and through data with innovation driven by layered modular architectures and recombination and provide a few directions along which these two rather different paradigms of innovation could be approached and likely reconciled.